Mixed EWMA-CUSUM Research Articles

THE MIXED UNIVARIATE CONTROL CHART EWMA AND CUSUM FOR FLAVOUR PRODUCTION QUALITY PROCESS MONITORING

A control chart is an important statistical technique used to monitor the average quality of a process or dispersion. Shewhart control chart is used to detect larger disturbances in process parameters. Along with the times, a more sensitive univariate control chart is created, namely EWMA and CUSUM. The control chart is developed into a combination as a Mixed EWMA-CUSUM control chart to detect smaller changes. The performance of the Mixed EWMA – CUSUM control graph does not only rely on current observations, but also collects information from previous observations so as to provide a fast signal to detect out of control conditions.

THE PERFORMANCES OF MIXED EWMA-CUSUM CONTROL CHARTS BASED ON MEDIAN-BASED ESTIMATORS UNDER NON-NORMALITY

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts have been regularly used to monitor small process mean shifts. More recently, a mixture of EWMA and CUSUM charts known as mixed EWMA-CUSUM (MEC) control chart has been introduced for better small shift detection. However, like its predecessor, the MEC chart requires the normality assumption to ensure optimal performances. In the presence of outliers, which is the cause of non-normality, the parameters of the chart may be overestimated, leading to an unreliable monitoring process. To mitigate this problem, this paper employed median-based estimators namely, the median and modified one-step M-estimator (MOM), to control the location parameter via the MEC control chart. In this study, the performance of robust MEC charts for Phase II monitoring of location was compared with the standard MEC chart that is based on the sample mean. The performance of the robust MEC charts in terms of the average run length (ARL) on various g-and-h distributions clearly shows that a robust MEC chart based on the MOM estimator performs well regardless of the distributional shapes.

Efficient Monitoring of a Parameter of Non-Normal Process Using a Robust Efficient Control Chart: A Comparative Study

The control chart is a fundamental tool in statistical process control (SPC), widely employed in manufacturing and construction industries for process monitoring with the primary objective of maintaining quality standards and improving operational efficiency. Control charts play a crucial role in identifying special cause variations and guiding the process back to statistical control. While Shewhart control charts excel at detecting significant shifts, EWMA and CUSUM charts are better suited for detecting smaller to moderate shifts. However, the effectiveness of all these control charts is compromised when the underlying distribution deviates from normality. In response to this challenge, this study introduces a robust mixed EWMA-CUSUM control chart tailored for monitoring processes characterized via symmetric but non-normal distributions. The key innovation of the proposed approach lies in the integration of a robust estimator, based on order statistics, that leverages the generalized least square (GLS) technique developed by Lloyd. This integration enhances the chart’s robustness and minimizes estimator variance, even in the presence of non-normality. To demonstrate the effectiveness of the proposed control chart, a comprehensive comparison is conducted with several well-known control charts. Results of the study clearly show that the proposed chart exhibits superior sensitivity to small and moderate shifts in process parameters when compared to its predecessors. Through a compelling illustrative example, a real-life application of the enhanced performance of the proposed control chart is provided in comparison to existing alternatives.

Robust Shewhart-CUSUM design for monitoring process mean using repetitive sampling

The present study initiates the use of repetitive sampling (RS) for CUSUM type statistics discussed by Riaz et al. (2017) and couples it with the Shewhart chart (termed as RS-SEC-TCC) by targeting two objectives, i.e. robustness to non-normality and detection of small to large mean shifts quickly. The dominance of the RS-SEC-TCC over its competitors has been established using both individual and overall performance metrics. The results indicate that the RS-SEC-TCC excels in identifying small to large mean shifts in both directions for symmetric and skewed distributions. The use of asymmetric decision intervals ensures that the RS-SEC-TCC is robust to skewed process distributions by eliminating the average run length (ARL) biased problem. The RS-SEC-TCC has also surmounted the weakness of the mixed EWMA-CUSUM TCC by enabling earlier detection of the larger shift. In terms of overall performance metrics, the RS-SEC-TCC is adopted as a benchmark chart. By producing more out-of-control signals than its competitors in a real-world application, the RS-SEC-TCC proves its usefulness in practice. Consequently, the proposed RS-SEC-TCC will be a useful process monitoring tool that can be relied upon by quality and industrial engineers.

On efficient change point detection using a step cumulative sum control chart

Control charts are widely used to monitor the stability of processes and Shewhart is the most commonly used type of chart because of the simplicity of its structure. To improve the performance, there are several modifications on control chart suggested since its proposal like cumulative sum and exponentially weighted moving average control charts. The cumulative sum chart accumulates all the deviations from target mean higher than a specific design parameter which can be used to controls the sensitivity of this chart. The optimal choice of this design parameter is half of the target shift size. This results into an optimal performance in terms of quick detection of shift that is equal to the target shift size. For shift sizes other than target, the cumulative sum chart loses its performance and becomes inferior to other control charts in terms of average run length. Since we rarely know the process shift size that is going to occur in future, this study proposes a revision in the structure of cumulative sum chart. The adjusted cumulative sum chart is shown to be very flexible for a wide range of shifts, when designed against a target shift size. The proposed adjusted cumulative sum control chart is compared with cumulative sum, exponentially weighted, combined Shewhart-CUSUM, progressive mean, double progressive mean and mixed EWMA-CUSUM control charts in terms of zero- and steady-state average run lengths. The superiority zones are identified and the results are supported by a real-life implementation of the proposed scheme.

Efficient Control Charting Scheme for the Process Location with Application in Automobile Industry

The recently introduced triple exponentially weighted moving average (TEWMA) chart is the extended form of the classical EWMA and double EWMA (DEWMA) charts. On the other hand, the auxiliary information-based (AIB) homogeneously weighted moving average ( HWMA AIB ) chart is used for the monitoring of process location shifts efficiently as compared to the HWMA chart. Combining TEWMA with HWMA features is a new idea and is not seen in the literature until now. So, the objective of this study is to combine the idea of HWMA AIB and TEWMA charts and propose an AIB triple HWMA, symbolized as THWMA AIB chart to further improve the process location shift monitoring. The proposed THWMA AIB chart is developed by combining the AIB double HWMA plotting statistic into the other HWMA chart. The numerical results are computed using the Monte Carlo simulation method. Average run length ( ARL ), relative ARL , performance comparison index, and extra quadratic loss are used as comparison tools for the proposed THWMA AIB chart with the classical EWMA, TEWMA, mixed HWMA-CUSUM (MHC), AIB EWMA ( EWMA AIB ), HWMA, double HWMA (DHWMA), HWMA AIB , AIB mixed EWMA-CUSUM ( MEC AIB ), and AIB mixed CUSUM-EWMA ( MCE AIB ) charts. Finally, a practical application is also provided for users to demonstrate the proposed study’s vitality.

On designing the two one-sided mixed EWMA-CUSUM monitoring schemes for the coefficient of variation with an application to the sintering process

The Coefficient of Variation (CV) has been applied to different fields to measure the relative variation of a variable. To monitor the quality characteristic of various manufacturing or service processes, the memory-type monitoring scheme has become an important role in practice. In this study, we investigate the performance of the memory-type scheme, a mixed structure of the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM), for monitoring the CV, denoted as the MEC-γ2 scheme. Moreover, another MEC-γ2 scheme with a new resetting technology, denoted as MREC-γ2 scheme, is constructed to improve the monitoring scheme’s sensitivity to large shifts in a process. The fast initial response (FIR) feature is incorporated into the proposed schemes to enhance the efficiency. The simulation results, based on the run length (RL) properties, show the superiority of the proposed monitoring schemes against some competitors, including the EWMA-γ2 and CUSUM-γ2. Finally, an illustrative example is presented using a real dataset from the sintering process.

Homogeneously Mixed Memory Charts with Application in the Substrate Production Process

The cumulative sum (CUSUM) and the exponentially weighted moving average (EWMA) charts are renowned classical memory charts used to monitor small and moderate shifts in the process(s). Mixed memory charts like mixed EWMA-CUSUM (MEC) and mixed CUSUM-EWMA (MCE) are the advanced forms of classical memory charts used to identify shifts quickly in process parameters (location and/or dispersion). Similarly, the homogeneously weighted moving average (HWMA) chart is used for improved process monitoring. It will be worthwhile to combine the HWMA chart features with the existing mixed memory (MCE and MEC) charts to enhance the effectiveness of the mixed memory charts. Therefore, we proposed new charts: mixed HWMA-homogeneously CUSUM (MHWHC) and mixed homogeneously CUSUM-HWMA (MHCHW) charts. The Monte Carlo simulations are used to evaluate the proposed charts’ effectiveness. The average run length (ARL) is utilized to compare the proposed MHWHC and MHCHW charts’ performance with existing charts such as classical CUSUM and EWMA, MEC, MCE, and HWMA charts. The comparison revealed that the proposed mixed charts are superior to the existing counterparts, specifically monitoring small and moderate shifts. Finally, a real-life application using the manufacturing process’s data set is also provided from a practical point of view.

Mixed memory control chart based on auxiliary information for simultaneously monitoring of process parameters: An application in glass field

Cumulative sum (CUSUM) and exponentially weighted moving (EWMA) control charts, known as memory control charts, are famous to monitor a small-to-moderate shift in the process parameters (location and/or dispersion). The EWMA control chart based on auxiliary information denoted as EWMAAIB(1) and EWMAAIB(2) are advanced forms of the classical EWMA control chart to monitor the process location and dispersion, respectively. Likewise, the combined mixed EWMA-CUSUM (CMEC) control chart is used to simultaneously monitor the process parameters. This study presents the CMEC control chart based on auxiliary information, symbolized as CMECAIB control chart for simultaneous monitoring of the process parameters. The proposed CMECAIB control chart used EWMAAIB(1) and EWMAAIB(2) control charts plotting statistics as inputs in the classical CUSUM control charts. The Monte Carlo simulation is used as a computational technique for numerical results. The proposed CMECAIB control chart based on average run length performance measure is evaluated against other control charts such as CMEC, combined double mixed EWMA-CUSUM, combined CUSUM, maximum double EWMA, maximum EWMA based on auxiliary information (MaxEWMAAIB) control and maximum Hybrid EWMA based on auxiliary information (MaxHEWMAAIB) control charts. The comparison revealed the superiority of the proposed CMECAIB control chart. Besides, the CMECAIB control chart performs better as the correlation coefficient increases. Likewise, the proposed CMECAIB control chart has a better diagnostic ability for possible directions of changes against other control charts. It is vital to mention that some existing control charts such as classical CUSUM, CMEC, and maximum CUSUM are special cases of proposed CMECAIB control chart with the specific parameter’s values. Finally, to demonstrate the vitality of the proposed study from a practical point of view, a real-life application in the glass bottle manufacturing industry is also provided for users and practitioners.

Developing Mixed EWMA-CUSUM and CUSUM-EWMA control charts based on MRSS and DRSS procedures

The mixed EWMA-CUSUM and CUSUM-EWMA control charts are among the control charts provided in recent years by combining two exponentially weighted moving average and cumulative sum charts for efficient monitoring of the process mean. In this paper, we extended these mixed control charts by using new median ranked set sampling and double ranked set sampling procedures. The performance of the proposed mixed control charts is evaluated through extensive Monte Carlo simulations in terms of average run length criterion and the results show the proposed charts outperform the similar charts for detecting different shifts in process mean. Furthermore, a real data-set is also presented for explaining the implementation of the proposed control charts.

Distribution-free mixed GWMA-CUSUM and CUSUM-GWMA Mann–Whitney charts to monitor unknown shifts in the process location

The Mann–Whitney (MW) test is one of the most important nonparametric tests used in the comparison of the location parameters of two populations. Unlike the t-test, the MW test can be used when the assumption of normality fails to hold. In this paper, the MW U statistic is used to construct two efficient distribution-free monitoring schemes, namely the mixed generally weighted moving average-cumulative sum (GWMA-CUSUM) MW U scheme (denoted as U-MGC) as well as its reversed version, i.e. the CUSUM-GWMA MW U scheme (denoted as U-MCG). The performances of the proposed schemes are investigated using the average run-length (ARL) and average extra quadratic loss (AEQL) values through extensive simulations. The newly proposed charts are found to be superior in small shifts detection than their competing (existing and others that are briefly introduced here) distribution-free Shewhart, EWMA, CUSUM, mixed EWMA-CUSUM, mixed CUSUM-EWMA and GWMA MW U charts in many situations. A real-life example is used to demonstrate the design and implementation of the new schemes.

Mixed EWMA–CUSUM chart for COM-Poisson distribution

In this article, we develop a mixed EWMA-CUSUM control chart for monitoring moderate and/or small shift in the process following the Conway Maxwell Poisson (COM-Poisson) distribution. To determine the ability and performance of the proposed mixed EWMA-CUSUM control chart, we evaluate the average run lengths and compare with different control charts. We will compare the efficiency of the proposed control chart over the existing control charts in terms of average run length. The results show an improvement in ARL when compared with the existing charts. A real example and a simulation study is also added to use the chart in the industry.

Assorted control charts: An efficient statistical approach to monitor pH values in ecotoxicology lab

AbstractPrimarily, three types of control charts are employed to observe the disturbances in the process parameters. The large shifts are detected efficiently by Shewhart's control chart, whereas for small and medium instabilities, cumulative sum and exponentially weighted moving average control charts are used. This study proposes an assorted approach to monitor small, medium, and large disturbances in a single control charting procedure. For the evaluation of the proposed assorted control chart, we have used various measures like average run length, standard deviation run length, extra quadratic loss, relative average run length, and performance comparison index. A comparison of the proposed assorted control chart is presented with some typical charts including the Shewhart, cumulative sum, exponentially weighted moving average control charts, and some advanced modification such as combined Shewhart‐EWMA (CSE), combined Shewhart‐CUSUM (CSC), mixed EWMA‐CUSUM (MEC), FIR EWMA, and adaptive EWMA (AEWMA). Finally, a real‐life application example is presented to monitor the pH level of water in an ecotoxicology lab.

In-control robustness comparison of different control charts

Control charts are widely used to monitor the process parameters. Proper design structure and implementation of a control chart requires its in-control robustness, otherwise, its performance cannot be fairly observed. It is important to know whether a chart is sensitive to disturbances to the model (e.g. normality under which it is developed) or not. This study, explores the robustness of Mixed EWMA-CUSUM (MEC) control chart for location parameter under different non-normal and contaminated environments and compares it with its counterparts. The robustness of the MEC scheme and counterparts is evaluated by using the run length distributions, and for better assessment not only is in-control average run length (ARL) used, but also standard deviation of run length (SDRL) and different percentiles – that is, 5th, 50th and 95th– are considered. A careful insight is necessary in selection and application of control charts in non-normal and contaminated environments. It is observed that the in-control robustness performance of the MEC scheme is quite good in the case of normal, non-normal and contaminated normal distributions as compared with its competitor’s schemes.

An EWMA monitoring scheme with a single auxiliary variable for industrial processes

An EWMA-type scheme, with a single auxiliary variable, is proposed.The ratio mean estimator is used to improve the performance of the classical EWMA chart for monitoring location parameter.The study shows that the proposed chart outperforms its existing counterparts.A real-life industrial example is provided. When using control charts to monitor manufacturing processes, Shewhart control chart is known to be useful for detecting transient shifts, while the EWMA and CUSUM charts are useful for detecting persistent shifts. The efficiency of EWMA chart in monitoring location parameter can be improved by using an auxiliary variable that is closely related to the variable of interest. In this paper, an EWMA-type scheme using ratio estimator is developed to further increase the effectiveness of the classical EWMA chart in monitoring the location parameter. The proposed procedure outperforms the classical EWMA and even the mixed EWMA-CUSUM chart, especially when there is a strong positive relationship between the variable of interest and the auxiliary variable. Finally, a real data set is used to show the implementation procedures of the proposed chart.

Monitoring of serially correlated processes using residual control charts

Control charts act as the most important tool for monitoring of process parameters. The assumption of independence that underpins the implementation of the charts is violated when process observations are correlated. The e ect of this issue can lead to the malfunctioning of the usual control charts by causing a large number of false alarms or slowing the detection ability of the chart in unstable situations. In this paper, weinvestigated the performance of the Mixed EWMA-CUSUM and Mixed CUSUM-EWMA charts for the ecient monitoring of autocorrelated data. The charts are applied to the residuals obtained from tting an autoregressive (AR) model to the autocorrelated observations. The performance of these charts is compared with the performances of the residual Shewhart, EWMA, CUSUM, combined Shewhart-CUSUM, and combinedShewhart-EWMA charts. Performance criteria such as Average Run Length (ARL) and Extra Quadratic Loss (EQL) are used for the evaluation and comparison of the charts. Illustrative examples are presented to demonstrate the application of the charts to serially correlated observations

Mixed Tukey EWMA-CUSUM control chart and its applications

Tukey control chart (TCC) is a popular choice for robust monitoring of process parameters. With the advancement in technology, we develop refined techniques that incorporate multiple aspects in a single structure. This article is a similar effort to design an improved charting structure in the form of mixed Tukey EWMA-CUSUM chart (namely MEC-TCC). We have investigated the performance of the proposed chart using different run length properties. We have observed that the proposed MEC-TCC design serves the dual objectives, namely the efficient detection of shifts and robustness against non-normality. The comparative analysis has revealed that the proposed scheme is an effective competitor to the existing counterparts, including classical Shewhart, EWMA, CUSUM, Tukey and some other variants such as mixed EWMA-CUSUM, Tukey EWMA, Tukey CUSUM. Moreover, the proposed design presents some of the aforementioned charts as special cases. For real life considerations, we have implemented the proposed and existing charts to two real life data sets, one related to air quality and the other one concerning smartphone accelerometer.

Mixed EWMA-CUSUM and mixed CUSUM-EWMA modified control charts for monitoring first order autoregressive processes

In practice most processes are known to produce autocorrelated observations. Autocorrelation degrades the performance of control charts by producing frequent false alarms when the process is stable or makes the charts respond slowly to the detection of out-of-control states. The effects due to autocorrelation can be eliminated by using modified charts. In this procedure, the control limits of the traditional charts are adjusted to account for the autocorrelation. In this paper, we present the Mixed EWMA-CUSUM and Mixed CUSUM-EWMA modified charts for monitoring correlated data. The performance of these charts are compared to existing modified charts such as the Shewhart, CUSUM, EWMA, combined Shewhart-CUSUM and combined Shewhart-EWMA schemes using the average run length, extra quadratic loss and relative average run length measures. Examples are given to illustrate how the charts perform.

A Mixed EWMA–CUSUM Control Chart for Weibull‐Distributed Quality Characteristics

The control charts have been widely used for process monitoring. Shewhart control chart has ability to detect large disturbances in the process. The EWMA and CUSUM charts have ability to detect a small change in the manufacturing process. In this paper, we will design a mixed EWMA–CUSUM control chart for Weibull‐distributed quality characteristics. The Weibull distribution is one of the most popular distributions used to model failure mechanism because of flexible selection of shape and scale parameters. A Monte Carlo simulation is developed to assess the average run lengths for in‐control and out‐of‐control process. The comparison revealed that the proposed mixed chart is more sensitive to detect a small shift in the process. Copyright © 2016 John Wiley & Sons, Ltd.

Improving the Performance of Exponentially Weighted Moving Average Control Charts

A control chart is a graphical tool used for monitoring a production process and quality improvement. One such charting procedure is the Shewhart-type control chart, which is sensitive mainly to the large shifts. For small shifts, the cumulative sum (CUSUM) control charts and exponentially weighted moving average (EWMA) control charts were proposed. To further enhance the ability of the EWMA control chart to quickly detect wide range process changes, we have developed an EWMA control chart using the median ranked set sampling (RSS), median double RSS and the double median RSS. The findings show that the proposed median-ranked sampling procedures substantially increase the sensitivities of EWMA control charts. The newly developed control charts dominate most of their existing counterparts, in terms of the run-length properties, the Average Extra Quadratic Loss and the Performance Comparison Index. These include the classical EWMA, fast initial response EWMA, double and triple EWMA, runs-rules EWMA, the max EWMA with mean-squared deviation, the mixed EWMA-CUSUM, the hybrid EWMA and the combined Shewhart–EWMA based on ranks. An application of the proposed schemes on real data sets is also given to illustrate the implementation and procedural details of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.